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The Multimedian Location Problem on a Network Exploiting Block Structure

Author

Listed:
  • Y. Xu

    (Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida 32611)

  • Richard L. Francis

    (Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida 32611)

  • Timothy J. Lowe

    (Department of Management Sciences, University of Iowa, Iowa City, Iowa 52242)

Abstract

The multimedian problem is to locate “distinguishable” new facilities on a connected network G so as to minimize a total cost, which is a sum of costs directly proportional to (a) network distances between new facilities and existing facilities at vertex locations and (b) distances between pairs of new facilities. By solving a related multimedian problem in polynomial time on the “blocking graph” of G , which is a tree, we obtain information which localizes each optimal new facility location to some vertex or block (maximal nonseparable subgraph) of G . The problem then decomposes into independent multimedian problems, one for each localizing block, which can be solved by using branch and bound and a vertex-optimality property.

Suggested Citation

  • Y. Xu & Richard L. Francis & Timothy J. Lowe, 1994. "The Multimedian Location Problem on a Network Exploiting Block Structure," Transportation Science, INFORMS, vol. 28(2), pages 116-124, May.
    • Handle: RePEc:inm:ortrsc:v:28:y:1994:i:2:p:116-124
    DOI: 10.1287/trsc.28.2.116
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